As the government shutdown came to a close last month, President Obama said Washington would have to "earn back the trust of the American people."

The president apparently has a lot of work to do on that front as well.

For the first time in his presidency, a majority of voters do not think Obama is "honest and trustworthy" according to a Quinnipiac poll released late Tuesday. In the survey, 52 percent of respondents said Obama was not honest, while only 44 percent said he was, a striking change from January 2011, when nearly two thirds of voters trusted the president.

Also worrisome for Obama, that sentiment extended across different demographics. Six in ten independents said they no longer trusted the president, while majorities in every age bracket — including the 18-to-29-year-olds who have long been Obama's most ardent supporters — said the president wasn't trustworthy.

It's a stunning reversal for a president who, even when voters didn't like how he was running the White House, still came off as an honest steward. During the government shutdown, for instance, polls found that voters were far more willing to trust Obama than his GOP rivals. And in October, voters believed the president was honest by a 54-41 split, per Quinnipiac, numbers that Mitt Romney would have killed for.

Yet ObamaCare's terrible rollout has greatly eroded that invaluable asset, possibly taking with it some of the president's leverage to negotiate with Congress in looming battles on immigration and the budget.

By all accounts, the debut of ObamaCare's online exchange marketplace, a central piece of the overall health-care law, was a disaster. As a result, six in 10 voters now say they don't approve of how Obama has handled health care, according to Quinnipiac.

The bigger blow to Obama's credibility, though, came when insurance companies began dropping coverage for thousands of Americans because their existing health-insurance plans did not meet ObamaCare's more rigorous standards. Obama famously (and repeatedly) vowed that people who liked their insurance plans could keep them.

"The president's promise apparently came with a very large caveat," he wrote. "'If you like your health-care plan, you'll be able to keep your health-care plan — if we deem it to be adequate.'"

Further, while ObamaCare is expected to drive down premiums in the insurance market as a whole, some Americans will actually see their out-of-pocket costs rise. That would, to some, appear to contradict Obama's claims that the health-care law would lead to big savings.

Perhaps as a result of such revelations, only 19 percent of respondents in the Quinnipiac poll said the quality of their health care would improve thanks to the Affordable Care Act. Forty-three percent, on the other hand, said the quality of their care would get worse.

Some Democrats — especially those with potentially difficult re-election campaigns next year — have begun to ding Obama for the apparent contradictions.

Rep. Kurt Schrader (D-Ore.) charged the president over the weekend with "grossly misleading the American public." And even Bill Clinton, though hardly Obama's closest political ally, took a swipe at him, saying he "should honor the commitment the federal government made to these people and let them keep what they got."

Feeling the heat, the president himself took the unusual step last week of issuing a public apology, saying in an interview with NBC, "I am sorry that [people who have lost coverage] are finding themselves in this situation based on assurances they got from me."

If voters don't come back around on the president, it could seriously hinder Obama's ability to wield the bully pulpit and score the big policy wins he's eyeing for the remainder of his term. Getting ObamaCare running smoothly — and soon — would be a big step in that direction.